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Control ENG HW_Part_17

# Control ENG HW_Part_17 - was considered to have all its...

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dt dH A R H R H 2 1 2 2 1 1 = - dt dH A R H 3 2 2 = where Q = q –q S H 1 = h 1 -h 1S H 1 = h 2 -h 2S H = h - h S Taking Laplace transforms ) ( ) ( ) ( 1 1 1 1 s H s A R s H s Q = - ---------(1) ) ( ) ( ) ( 2 2 2 2 1 1 s H s A R s H R s H = - --------(2) ) ( ) ( 3 2 2 s H s A R s H = ----------(3) We have three equations and 4 unknowns(Q(s),H(s),H 1 (s) and H 2 (s). So we can express one in terms of other. From (3) s A R s H s H 3 1 2 2 ) ( ) ( = -------------(4)

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) 1 ( ) ( ) ( 2 1 1 2 2 + = s R s H R s H τ where 2 2 2 A R = τ ------------(5) From (1) ) 1 ( ) ( ) ( 1 1 1 + = s s Q R s H τ , 1 1 1 A R = τ ---------(6) Combining equation 4,5,6 ) 1 )( 1 )( ( ) ( ) ( 2 1 3 + + = s s s A s Q s H τ τ ) 1 )( 1 )( ( 1 ) ( ) ( 2 1 3 + + = s s s A s Q s H τ τ Above equation can be written as i.e, if non interacting first order system are there in series then there overall transfer function is equal to the product of the individual transfer function in series. 7.2 The mercury thermometer in
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Unformatted text preview: was considered to have all its resistance in the convective film surrounding the bulb and all its capacitance in the mercury. A more detailed analysis would consider both the convective resistance surrounding the bulb and that between the bulb and mercury. In addition , the capacitance of the glass bulb would be included. Let Ai = inside area of bulb for heat transfer to mercury. Ao = outside area of bulb, for heat transfer from surrounding fluid. .m = mass of the mercury in bulb. m b = mass of glass bulb. C = heat capacitance of mercury....
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